The structural phase transformations of $0.7Pb(Mg_{1/3}Nb_{2/3})O_3-0.3PbTiO_3$ (PMN-0.3PT) were studied using high resolution x-ray diffraction (HRXRD) as a function of temperature and electric field. A phase transformational sequence of cubic (C)${ ightarrow}$tetragonal (T)${ ightarrow}$rhombohedral (R) phase was observed in zero-field-cooled conditions; and a $C{ ightarrow}T{ ightarrow}$monoclinic $(M_C){ ightarrow}$ monoclinic ($M_A$) phase was observed in the field-cooled conditions. The transformation of T to $M_A$ phase was realized through an intermediate $M_C$ phase. The results also represent conclusive and direct evidence of a $M_C$ to $M_A$ phase transformation in field-cooled conditions. Beginning from the zero-field-cooled condition, a $R{ ightarrow}M_A{ ightarrow}M_C{ ightarrow}T$ phase transformational sequence was found with an increasing electric field at a fixed temperature. Upon removal of the field, the $M_A$ phase was stable at room temperature. With increasing the field, the transformation temperature from T to $M_C$ and from $M_C$ to $M_A$ phase decreased, and the phase stability ranges of both T and $M_C$ phases increased. Upon removal of the field, the phase transformation from R to $M_A$ phase was irreversible, but from $M_A$ to $M_C$ was reversible, which means that $M_A$ is the dominant phase under the electric field. In the M phase region, the results confirmed that lattice parameters and tilt angles were weakly temperature dependent over the range of investigated temperatures.